Micky van de Ven Double Ends The Toffees' Run at New Home Ground
The Dutch defender became the first backline player to score twice in a Premier League game for Tottenham since the Belgian defender in March 2013.
Match summary
The Spurs defender heads into the net two times in first half
Everton's Jake O'Brien has equalizer ruled after video check
Senegalese midfielder nets final goal in 89th minute
The defeat is Everton's initial at Hill Dickinson Stadium
Micky van de Ven scored twice as Spurs extended their unbeaten run on the road in the Premier League and handed the Toffees their initial loss at Hill Dickinson Stadium.
Everton were unbeaten in their five previous fixtures at their recently opened stadium at Bramley-Moore Dock, having left their historic home behind after more than a century at the conclusion of the previous campaign.
But Tottenham's leader the Dutchman struck twice from set-pieces in the opening 45 minutes to place their impressive record at jeopardy, and they were failed to mount a comeback before the midfielder - assisted by ex-Everton forward Richarlison - nodded in a final goal to seal the victory.
Jake O'Brien believed he had equalized the tally five minutes after Van de Ven's first goal, glancing a powerful header past the Spurs keeper from an set-piece.
Beto, in the meantime, failed to convert a handful of opportunities, while Vicario made a series of fine saves to guarantee Tottenham went five away games without defeat in the English top flight.
But the VAR stepped in, advising Craig Pawson to check the goal on the pitchside monitor and the official decided that Jack Grealish and the attacker were in an illegal position and had interfered with the Spurs keeper.
The win moves the manager's team into third place in the division, a handful of points off north London rivals and leaders the Gunners.
Everton stay in 14th position and are six points clear of the drop zone.
Tottenham analysis: The defender excels in role at both ends of the field
After a uninspiring midweek performance in the Champions League against the French side, where they mustered a only two shots on goal, the manager opted for the French striker in attack instead of former Toffees player the Brazilian.
The summer signing was unable to influence the game before being substituted for Richarlison after an hour on the pitch, but it turns out he wasn't needed in the end.
Centre-back the Dutchman transformed into an attacking force to be reckoned with.
Tottenham's opening strike came from a well-worked set-piece play, with Rodrigo Bentancur heading the ball toward the six-yard box for an unmarked the defender to head home.
And the captain - filling in as skipper in the Argentine's absence - notched his next goal in added time as he rose above Jordan Pickford to nod in.
Van de Ven was just as outstanding in defence, combining well with Kevin Danso as the pair dealt superbly with the numerous deliveries thrown their way by Everton.
Everton analysis: Everton missing finishing touch
Everton's new home had been a fortress, but it seems the freshness may have faded somewhat and fans flocked to the gates after Sarr's final goal for Tottenham.
The break in Everton's winning streak at home will not be a massive concern for David Moyes, but their attacking woes will be.
The forward and the other striker - the Everton's two established strikers - had scored just one league goal between them before Sunday's outing.
And they were failed to contribute to that miserable record on a wet and gloomy night on in Liverpool.
Beto's performance was summed up when he chose to bicycle-kick a golden opportunity from near the goal, despite having space and opportunity to readjust for a more conventional attempt that would have tested the keeper.
The substitute, as well, was unable to influence the game after coming on for the starter in the second half.
It was not for a shortage of chance. The majority of the home side's offensive moves came through Grealish and Ndiaye, who tirelessly whipped dangerous crosses into the Tottenham penalty area.
Upcoming fixtures for these two sides?
Everton: The team travel to Sunderland in the Premier League on Monday, 3 November at 20:00 GMT.
Tottenham: The London club go to St James' Park on late October for their next round League Cup tie against Newcastle.